In algebra, “log” is short for “logarithm.” Logarithms are the opposites, or inverses, of equations involving exponents, like y = x^3. In their simplest form, logs help to determine how many of one number must be multiplied to obtain another number. Logarithms were initially invented to help people solve lengthy calculations at a time before calculators existed. In the modern era, they are used to solve a variety of real-world problems ranging from compound interest to population growth to radioactive decay.

Representation and Equivalence

Logs are described symbolically by the equation log(b)(y) = x. This is generally pronounced “log base b of y is x.” It is equivalent to the exponential equation y = b^x, in which “b” represents the base number and “x” represents the exponent. In any logarithm, the base, b, must be greater than zero and cannot equal one. Sometimes, there is no base written -- in this case, assume that the base is 10.

How Logs Work

Oftentimes in algebra, seeing an example with actual numbers helps to make a concept clearer. Consider the example of log(5)(125) = 3. What this means in terms of exponents is that 5^3 = 125, or 5 x 5 x 5 = 125. So, if a variable were present in a logarithmic equation, the equation could be solved using exponents. For instance, suppose a problem necessitated finding “y” in log(2)(y) = 4. This could be easily solved by simplifying 4^2, resulting in a solution of 16.

Resources

Photo Credits

Duncan Smith/Photodisc/Getty Images

About the Author

Based in western New York, Amy Harris began writing for Demand Media and Great Lakes Brewing News in 2010. Harris holds a Bachelor of Science in Mathematics from Penn State University; she taught high school math for several years and has also worked in the field of instructional design.